The gravitational waves from a binary inspiral carry unique information about the internal structure of compact objects. This information is of major interest for neutron stars, offering the possibility for advancing our understanding matter and fundamental interactions in unexplored regimes. I will discuss the imprints of an object’s internal structure, and in particular neutron star matter, on the gravitational waves generated during an inspiral, methods for analytically modeling these effects, and what we have learned from GW170817. I will also outline future prospects and challenges.